Question

For what irrational value of $x$ can three numbers, $0.\left(27\right),x$ and $0.\left(72\right)$ form a progression (arithmetic or geometric)? Find $x$ and the sum of four terms of the progression.

Answer 1

For Arithmetic Progression

$2x=.27+.72$

$⟹x=.495$

sum of four terms is $2.43$